Finite Group Databasebeta

← #25000093

Subgroups — #25000093

Order 11008.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135565C212yesmaximal
2#19134764C211yesmaximal, characteristic
3C2×#14582641C212yesmaximal
4#19132476C211yesmaximal, characteristic
5C43×#2822C211yesmaximal, characteristic
6C2×#13063258—21no—
7C2×#13063256—21no—
8C2×#13063236C2212yes—
9C2×#13063236C2211yescharacteristic
10#14582769C2211yescharacteristic
11#14582661—22no—
12#14582661—22no—
13#14582641—24no—
14C2×#125×C43C2212yes—
15C43×#400—22no—
16C43×#398—21no—
17C43×#398—21no—
18C43×#398—22no—
19C43×#382C2211yescharacteristic
20C22×C43⋊C8—21no—
21C22×C43⋊C8—22no—
22C2×C4⋊Dic43—22no—
23C2×C4⋊Dic43—21no—
24#13063258—42no—
25#13063256—42no—
26#13063236—21no—
27#13063236—22no—
28#13063236—22no—
29#13063236D412yes—
30#125×C43—22no—
31#125×C43—22no—
32#125×C43—22no—
33#125×C43—22no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43D412yes—
39C2×C4⋊C4×C43D412yes—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C42×C43C2311yescharacteristic
43#95×C43—22no—
44#95×C43—22no—
45#95×C43—21no—
46#95×C43—21no—
47#95×C43—22no—
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43C2×D412yes—
53C22×C4×C43C2×D411yescharacteristic
54C22×Dic43—41no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—41no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—81no—
66C4⋊C4×C43—81no—
67C42×C43C2×D411yescharacteristic
68C42×C43#4111yescharacteristic
69C42×C43#4112yes—
70C4⋊Dic43—41no—
71C4⋊Dic43—41no—
72C4⋊Dic43—44no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—22no—
75C2×C43⋊C8—22no—
76C2×C43⋊C8—24no—
77C2×C43⋊C8—42no—
78C2×C43⋊C8—42no—
79C23×C43#12011yescharacteristic
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—42no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43—42no—
93C2×C4×C43—42no—
94C2×C4×C43#12111yescharacteristic
95C2×C4×C43#12112yes—
96C2×C4×C43#12312yes—
97C2×C4×C43#12411yescharacteristic
98C2×Dic43—81no—
99C2×Dic43—82no—
100C43⋊C8—24no—
101C43⋊C8—44no—
102#10429—431nomaximal, Sylow
103C22×C43#39411yescharacteristic
104C22×C43#45311yescharacteristic
105C22×C43#45412yes—
106C22×C43#45612yes—
107C22×C43#45611yescharacteristic
108C4×C43—22no—
109C4×C43—22no—
110C4×C43—21no—
111C4×C43—21no—
112C4×C43—81no—
113C4×C43—81no—
114C4×C43—82no—
115C4×C43—82no—
116Dic43—161no—
117#2822D4311yescharacteristic
118#1992—432no—
119#1847—431no—
120C2×#330—432no—
121#1295—431no—
122C2×C43#165711yescharacteristic
123C2×C43#166011yescharacteristic
124C2×C43#166312yes—
125C2×C43#203812yes—
126C2×C43#203911yescharacteristic
127C2×#125C2×D4312yes—
128C2×#107—861no—
129C2×#106—861no—
130C2×#97—431no—
131C2×#97—432no—
132#400—22no—
133#398—21no—
134#398—21no—
135#398—22no—
136#384—431no—
137#382C2×D4311yescharacteristic
138#340—862no—
139#340—862no—
140#330—864no—
141C43#1042911yescharacteristic, complemented, Sylow
142C22×C8—861no—
143C22×C8—862no—
144#125—22no—
145#125—22no—
146#125—22no—
147#125—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—862no—
153C2×C4⋊C4—861no—
154C2×C4⋊C4C22⋊D4312yes—
155C2×C4⋊C4C22⋊D4312yes—
156C2×C4⋊C4C22⋊D4311yescharacteristic
157C2×C4⋊C4C22⋊D4311yescharacteristic
158C2×C42C22×D4311yescharacteristic
159#107—1722no—
160#106—1722no—
161#97—432no—
162#97—862no—
163#97—861no—
164#97—862no—
165#95—22no—
166#95—22no—
167#95—21no—
168#95—21no—
169#95—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—1721no—
175C22×C4C2×C22⋊D4311yescharacteristic
176C22×C4C2×C22⋊D4312yes—
177C2×C8—862no—
178C2×C8—862no—
179C2×C8—862no—
180C2×C8—864no—
181C2×C8—1722no—
182C2×C8—1722no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—1721no—
196C4⋊C4—1721no—
197C4⋊C4—1724no—
198C42D4×D4311yescharacteristic
199C42#1062190011yescharacteristic
200C42#1062190012yes—
201C23#1306329411yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—3441no—
217C2×C4—3442no—
218C2×C4#1306329611yescharacteristic
219C2×C4#1306329712yes—
220C2×C4#1306330612yes—
221C2×C4#1306331211yescharacteristic
222C8—864no—
223C8—1724no—
224C22#1458281311yescharacteristic
225C22#1458306711yescharacteristic
226C22#1458307212yes—
227C22#1458308212yes—
228C22#1458308211yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—82no—
234C4—82no—
235C4—81no—
236C4—81no—
237C4—6881no—
238C2#1913389311yescharacteristic
239C2#1913390611yescharacteristic
240C2#1913392312yes—
241C2#1913580912yes—
242C2#1913581611yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2822C2
socle, prime radicalC23×C43#120
hypercenter#2822D43
hypocenterC43#10429
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
141. C43#10429semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191355652
#191347642
C2×#145826412
#191324762
C43×#28222
#1042943